1. ## Make a table...

Make a table showing all the values of the functions u4 : Z15 ->Z15.

The function u
a defined by the rule x ->ax is a bijection Zm ->Zm.

How is this done? Thanks...

2. Originally Posted by jzellt
Make a table showing all the values of the functions u4 : Z15 ->Z15.

The function u
a defined by the rule x ->ax is a bijection Zm ->Zm.

How is this done? Thanks...
$\displaystyle (4,15)=1 \implies \{4\cdot1, 4\cdot2,\cdot\cdot\cdot, 4\cdot 15\} = \{1,2,\cdot\cdot\cdot,15\}$

Therefore $\displaystyle u_4(\mathbb{Z}_{15}) = \mathbb{Z}_{15}$.

$\displaystyle \begin{array}{r|r||r|r}a&u_4(a)&a&u_4(a)\\ \hline 0&0&8&2\\1&4&9&6\\2&8&10&10\\3&12&11&14\\4&1&12&3\ \5&5&13&7\\6&9&14&11\\7&13\end{array}$

3. Thanks for the quick reply, but I'm still not seeing what my table should look like...

4. Originally Posted by chiph588@
$\displaystyle \begin{array}{r|r||r|r}a&u_4(a)&a&u_4(a)\\ \hline 0&0&8&2\\1&4&9&6\\2&8&10&10\\3&12&11&14\\4&1&12&3\ \5&5&13&7\\6&9&14&11\\7&13\end{array}$
Here you go.